Two-State Bulk Queueing Models with Multiple Vacations

In the present work we study the transient behavior of some two-state bulk queueing models with (i) Intermittently available server, i.e. the server goes either for rest or to attend some very urgent jobs when the queue length is greater than or equal to zero. The server has the option to start a fresh service instantaneously or to make interruption, but it is assumed that he completes the service in hand before the interruption, (ii) Multiple vacations, i.e. the server begins a vacation with probability one each time the system becomes empty. If the server returns from a vacation to find the system not empty. If the server returns from a vacation to find no customers waiting, it begins another vacation immediately, and continues in this manner until it finds at least one customer waiting upon returning from a vacation (multiple vacations), and (iii) Non- exhaustive service, i.e. the server may go on vacation even if there are some customers waiting for service or vacations may start even when customers are present in the system.